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A192087 Potential magic constants of a 10 X 10 magic square composed of consecutive primes. 1
2862, 3092, 3500, 4222, 4780, 5608, 7124, 10126, 10198, 11212, 11426, 12140, 12212, 12284, 12356, 12428, 12714, 12854, 12924, 15270, 16252, 16476, 18594, 18672, 18750, 18828, 19214, 20764, 21150, 23752, 24214, 24598, 24828, 27180, 27342, 27424, 27916, 28666, 29406, 29568 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For a 10 X 10 magic square composed of 100 consecutive primes, the sum of these primes must be a multiple of 20.
This sequence consists of even integers equal the sum of 100 consecutive primes divided by 10. It is not known whether each such set of consecutive primes can be arranged into a 10 X 10 magic square but it looks plausible.
Actual magic squares were constructed for all listed magic constants <= 11212.
LINKS
Natalia Makarova, Sequence of Magic Numbers MK 10th Order (in Russian).
EXAMPLE
a(1)=2862 for a square containing prime(9)..prime(108):
[23 179 409 373 263 137 461 457 523 37
193 353 443 199 317 109 337 397 131 383
71 73 389 251 593 167 439 449 233 197
571 293 101 229 29 557 271 31 379 401
127 419 283 241 269 239 547 89 181 467
491 433 223 113 41 577 43 311 563 67
281 97 163 587 191 313 149 509 421 151
307 499 227 431 103 83 59 479 211 463
277 359 257 331 569 541 53 79 47 349
521 157 367 107 487 139 503 61 173 347]
.
a(10)=11212
[769 863 1171 967 859 1381 1237 1459 1289 1217
1163 953 797 1297 1049 1021 1303 977 1423 1229
809 1277 1153 937 1151 1409 1291 839 1249 1097
1429 1231 1193 1451 1061 829 821 1361 823 1013
1453 997 947 1091 1321 887 1283 941 811 1481
1069 1201 1427 1129 907 919 1373 1039 1117 1031
1009 1123 1301 1093 1367 1483 911 1051 1087 787
991 1109 1279 877 1223 929 1187 1433 1327 857
1213 1439 1063 971 1447 883 773 1259 983 1181
1307 1019 881 1399 827 1471 1033 853 1103 1319]
MAPLE
s:= proc(n) option remember;
`if` (n=1, add (ithprime(i), i=1..100),
ithprime(n+99) -ithprime(n-1) +s(n-1))
end:
a:= proc(n) option remember; local k, m;
a(n-1);
for k from 1+b(n-1) while irem (s(k), 20, 'm')<>0 do od;
b(n):= k; m
end:
a(0):=0: b(0):=0:
seq (2*a(n), n=1..50);
CROSSREFS
Sequence in context: A031603 A236586 A233379 * A286007 A235960 A235571
KEYWORD
nonn
AUTHOR
Natalia Makarova, Jun 23 2011
STATUS
approved

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Last modified July 21 00:40 EDT 2024. Contains 374462 sequences. (Running on oeis4.)